Question

If y=x^3+2x and dx/dt=5, find dy/dt when x=2. Give only the numerical answer. @freckles

Answer 1

can you find dy/dx ?

Answer 2

yes y'=3x^2+2x
@freckles

Answer 3

dy/dx=3x^2+2

Answer 4

\[\frac{dy}{dx}=\frac{dy}{dt} \cdot \frac{dt}{dx}\]

Answer 5

\[3x^2+2=\frac{dy}{dt} \cdot \frac{dt}{dx}\]

Answer 6

you are given dx/dt=5
so dt/dx=1/5

Answer 7

and this occurs when x=2

Answer 8

\[3(2)^2+2=\frac{dy}{dt} \cdot \frac{1}{5}\]

Answer 9

can you solve for dy/dt

Answer 10

doesd dy/dt=70

Answer 11

if i did my basic algebra correctly that is what i got

Answer 12

\[y=x^3+2x\]
diff. with respect to t
\[\frac{ dy }{ dt }=3x^2\frac{ dx }{ dt }+2\frac{ dx }{ dt }\]
substitute the given values